Omics technologies are powerful tools for analyzing patterns in gene expression data for thousands of genes. Due to a number of systematic variations in experiments, the raw gene expression data is often obfuscated by undesirable technical noises. Various normalization techniques were designed in an attempt to remove these non-biological errors prior to any statistical analysis. One of the reasons for normalizing data is the need for recovering the covariance matrix used in gene network analysis. In this paper, we introduce a novel normalization technique, called the covariance shift (C-SHIFT) method. This normalization algorithm uses optimization techniques together with the blessing of dimensionality philosophy and energy minimization hypothesis for covariance matrix recovery under additive noise (in biology, known as the bias). Thus, it is perfectly suited for the analysis of logarithmic gene expression data. Numerical experiments on synthetic data demonstrate the method's advantage over the classical normalization techniques. Namely, the comparison is made with Rank, Quantile, cyclic LOESS (locally estimated scatterplot smoothing), and MAD (median absolute deviation) normalization methods. We also evaluate the performance of C-SHIFT algorithm on real biological data.

We propose a distributed data replenishment mechanism for some distributed peer-to-peer-based storage systems that automates the process of maintaining a sufficient level of data redundancy to ensure the availability of data in presence of peer departures and failures. The dynamics of peers entering and leaving the network are modeled as a stochastic process. A novel analytical time-backward technique is proposed to bound the expected time for a piece of data to remain in P2P systems. Both theoretical and simulation results are in agreement, indicating that the data replenishment via random linear network coding (RLNC) outperforms other popular strategies. Specifically, we show that the expected time for a piece of data to remain in a P2P system, the longer the better, is exponential in the number of peers used to store the data for the RLNC-based strategy, while they are quadratic for other strategies.

We derive theoretical performance limits of densely covered delay-tolerant networks (DTNs). In the DTN model we study, a number of fixed (data collector) nodes are deployed in the DTN region where mobile (data generator) nodes move freely in the region according to Brownian motion. As it moves, each mobile is assumed to continuously generate and buffer data. When a mobile comes within the communication coverage range of a data collector node, the mobile immediately and completely uploads its buffered data to the data collector node, and then resumes generating and buffering its data. In this paper, we first derive analytic bounds on the amount of time a mobile spends without communication coverage. Then, using these derived bounds, we derive sufficient conditions on node density that statistically guarantee that the expected amount of time spent in the uncovered region remains below a given threshold. Additionally, we derive sufficient conditions on node density to keep the probability of buffer overflow below a given tolerance.

We derive theoretical bounds on expected hitting times in densely covered delay-tolerant networks (DTNs). We consider a number of fixed (data collector) nodes deployed in the DTN region, and a number of mobile (data generator) nodes that move freely in the region according to Brownian motion. As it moves, each mobile node is assumed to continuously generate and buffer data. When a mobile node comes within the communication coverage range of a data collector node, it downloads its buffered data to it. Otherwise, it keeps generating and buffering its data. In this paper, we derive analytic bounds on the amount of time a mobile node spends without communication coverage. Then, using these derived bounds, we derive sufficient conditions on node density that statistically guarantee that the expected hitting times remain below a given threshold.

This paper is concerned with the design and analysis of delay-tolerant networks (DTNs) deployed for free-roaming animal monitoring, wherein information is either transmitted or carried to static access-points by the animals whose movement is assumed to be random. Specifically, in such mobility-aided applications where routing is performed in a store-carry-and-drop manner, limited buffer capacity of a carrier node plays a critical role, and data loss due to buffer overflow heavily depends on access-point density. Driven by this fact, our focus in this paper is on providing sufficient conditions on access-point density that limit the likelihood of buffer overflow. We first derive sufficient access-point density conditions that ensure that the data loss rates are statistically guaranteed to be below a given threshold. Then, we evaluate and validate the derived theoretical results through comparison with both synthetic and real-world data.

This paper investigates the performance limits of delay tolerant networks (DTNs) with intermittently connected nodes deployed for wildlife monitoring, wherein information is either transmitted or carried to static accesspoints by free-ranging animals whose movement is assumed to be random. Specifically, in such mobility-aided applications where routing is performed in a store-carry-and-drop manner, limited buffer capacity of a carrier node plays a critical role, and data loss due to buffer overflow heavily depends on access-point density. Driven by this fact, our focus in this paper is on providing sufficient conditions on accesspoint density that limit the likelihood of buffer overflow. Specifically, we first derive and prove sufficient access-point density conditions that ensure that the data loss rates are statistically guaranteed to be below a given threshold. We consider studying both the square and hexagonal accesspoint deployment structures. Then, we validate the derived theoretical results for each of the two studied structures through simulations.

We characterize some fundamental performance limits of partially covered, intermittently connected, delay-tolerant networks (DTNs) that are comprised of a hybrid mix of mobile and static nodes (i.e., access points). Specifically, we derive theoretic bounds on the expected hitting time between two consecutive visits of a mobile node to access points for both the square and hexagonal access point deployment structures. For each of these two models, we use the Poisson Clumping technique to derive theoretic bounds on the data loss rate, under the assumption that a mobile node has a finite buffer that overflows after a certain amount of time. Based of these obtained results, we provide asymptotic analysis of the expected hitting time in these partially covered DTNs. We test the applicability of the Poisson Clumping technique, and our hitting time results, with simulations.

We investigate a class of randomized peer-to-peer (P2P) approach to Internet-wide distributed data storage systems that promises to reduce the coordination complexity and increases performance scalability. The core of these randomized P2P data storage systems is the data replenishment mechanism. The data replenishment automates the process of maintaining a sufficient level of data redundancy to ensure the availability of data in presence of peer departures and failures. The dynamics of peers entering and leaving the network is modeled as a stochastic process. A novel analytical time-backward technique is proposed to bound the expected time for a piece of data to remain in P2P systems. Both theoretical and simulation results are in agreement, indicating that a proposed data replenishment via random linear network coding (RLNC) outperforms other strategies that employ popular repetition and channel coding techniques. Specifically, we show that the expected time for a piece of data to remain in a P2P system, the longer the better, is exponential in the redundancy amount for the RLNC-based strategy, while they are quadratic for other strategies.

Current video streaming and storage systems such as YouTube, are based on the client-server model, thus do not scale well in terms of bandwidth and computation. This paper describes a peer-to-peer video delivery network (P2P-VDN) that provides both performance improvement and scalability based on three architectural elements. First, the proposed P2P-VDN employs a random network coding (RNC) scheme that breaks a video stream into multiple smaller pieces, codes, and disperses them throughout peers in the network, in such a way to maximize the probability of recovering the original video under peer departures and failures. Second, the proposed P2P-VDN employs a scalable mechanism for automating the data replenishment process using RNC that is necessary to maintain a sufficient level of redundancy for video stored in the network. Third, the proposed P2P-VDN employs a path-diversity protocol for a client to simultaneously stream a video from multiple peers in the P2P-VDN. Simulations demonstrate that under certain scenarios, our proposed P2P-VDN can result in bandwidth saving up to 60% over the traditional architecture.